To calculate the work done in lifting an object against gravity, you can use the formula:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
In this case:
- The force is equal to the weight of the object, which can be calculated as:
\[ \text{Force} = \text{mass} \times g \]
where \( g \) (acceleration due to gravity) is approximately \( 9.81 , \text{m/s}^2 \).
- The distance is the height the object is lifted, which is \( 3 , \text{m} \).
- Since the force is applied in the same direction as the displacement when lifting the object, \( \theta = 0^\circ \), and \( \cos(0)=1 \).
Now, substituting the values:
-
Calculate the force (weight of the object): \[ \text{Force} = 4 , \text{kg} \times 9.81 , \text{m/s}^2 = 39.24 , \text{N} \]
-
Calculate the work done: \[ \text{Work} = 39.24 , \text{N} \times 3 , \text{m} \times \cos(0) = 39.24 , \text{N} \times 3 , \text{m} = 117.72 , \text{J} \]
Therefore, the work done in lifting the object is \( 117.72 , \text{J} \).
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